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SCHAUMBURG, Ill. (AP) - Mitt Romney took a major stride toward the Republican presidential nomination Tuesday night, routing Rick Santorum in the Illinois primary for his third big-state win in a row and padding his already-formidable lead in the race for convention delegates.

"What a night," Romney exulted to cheering supporters in suburban Chicago. Looking beyond his GOP rivals, he said he had a simple message for President Barack Obama, the man Republicans hope to defeat next fall: "Enough. We've had enough."

That was a far more substantial showing for Romney than the grudging victories he eked out in the previous few weeks in Michigan and Ohio, primaries that did as much to raise questions about his ability to attract Republican support as to quell those questions.

Santorum, who hopes to rebound in next Saturday's Louisiana primary, sounded like anything but a defeated contender as he spoke to supporters in Gettysburg, Pa. He said he had outpolled Romney in downstate Illinois and the areas "that conservatives and Republicans populate. We're very happy about that and we're happy about the delegates we're going to get, too."

"Saddle up, like (Ronald) Reagan did in the cowboy movies," he urged his backers.

Romney triumphed in Illinois after benefiting from a crushing, 7-1 advantage in the television advertising wars, and as his chief rival struggled to overcome self-imposed political wounds in the marathon race to pick an opponent to Obama.

Most recently, Santorum backpedaled after saying on Monday that the economy wasn't the main issue of the campaign. "Occasionally you say some things where you wish you had a do-over," he said later.

Over the weekend, he was humbled in the Puerto Rico primary after saying that to qualify for statehood the island commonwealth should adopt English as an official language.

Romney's victory was worth at least 41 delegates in Illinois, while Santorum won 10. The two rivals were battling for the final three delegates but the results were too close to call on election night.

Romney has 563 in the overall count maintained by The Associated Press, out of 1,144 needed to win the nomination. Santorum has 263 delegates, Gingrich 135 and Paul 50.

Exit polls showed Romney preferred by primary goers who said the economy was the top issue in the campaign, and overwhelmingly favored by those who said an ability to defeat Obama was the quality they most wanted in a nominee.

He won among votes who said they were somewhat conservative or moderate, while Santorum prevailed among those who said they were "very conservative."

While pre-primary polls taken several days ago in Illinois suggested a close race, Romney and Restore Our future, a super Pac that backs him, unleashed a barrage of campaign ads to erode Santorum's standing. One ad accused the former Pennsylvania senator of changing his principles while serving in Congress, while two others criticized him for voting to raise the debt limit, raise his own pay as a lawmaker and side with former Sen. Hillary Rodham Clinton to support legislation allowing felons the right to vote.

In all, Romney and Restore Our Future outspent Santorum and a super PAC that backs him by $3.5 million to $500,000, an advantage of 7-1.

In the long and grinding campaign, Santorum looked to rebound in next Saturday's primary in Louisiana, particularly given Romney's demonstrated difficulties winning in contests across the Deep South.

A 10-day break follows before Washington, D.C., Maryland and Wisconsin hold primaries on April 3.

Santorum is not on the ballot in the nation's capital.

Private polling shows Romney with an advantage in Maryland, and Restore Our Future launched a television ad campaign in the state during the day at a cost of more than $450,000.

Wisconsin shapes up as the next big test between Romney and Santorum, an industrial state next door to Illinois, but one where Republican politics have been roiled recently by a controversy involving a recall battle against the governor and some GOP state senators who supported legislation that was bitterly opposed by labor unions.

Already, Restore Our future has put down more than $2 million in television advertising across Wisconsin. Santorum has spent about $50,000 to answer.

Gingrich has faded into near-irrelevance in the race, but he was defiant in a statement issued after Romney sealed his victory.

"To defeat Barack Obama, Republicans can't nominate a candidate who relies on outspending his opponents 7-1. Instead, we need a nominee who offers powerful solutions that hold the president accountable for his failures," it said.

Gingrich said his campaign will spend the time leading to the party convention "relentlessly taking the fight to President Obama."

Illinois fell into Romney's column far more easily than Michigan or Ohio had.

The night's vote count was plagued by ballot difficulties. Rupert Borgsmiller, executive director, of the Illinois State Board of Elections, said in late afternoon that 25 counties and the city of Aurora were affected by the ballot problem. He didn't know how many ballots were affected but said "clearly you can say more than hundreds."

Romney and Santorum campaigned energetically across the state, and not always in respectful tones.

"Senator Santorum has the same economic lightweight background the president has," Romney said at one point. "We're not going to replace an economic lightweight with another economic lightweight."

Anticipating a primary defeat, Santorum's campaign argued that the race for delegates is closer than it appears.

Santorum contends the Republican National Committee at the convention will force Florida and Arizona to allocate their delegates on a proportional basis instead of winner-take-all as the state GOP decided. Romney won both states.

On Tuesday, about four in 10 voters interviewed as they left their polling places said they were evangelical or born again. That's about half the percentage in last week's primary states of Alabama and Mississippi, where Santorum won narrowly. Despite an unusually lengthy race for the nomination, less than a third of those voting said in the polling-place survey they hoped the primary season would come to a quick end even if that meant their candidate might lose the nomination.

The findings came from preliminary results from the survey of 1,555 Illinois Republican voters, and had a margin of error of plus or minus 4 percentage points. The exit poll was conducted for The Associated Press and the television networks by Edison Research at 35 randomly selected polling places around the state.

As Illinois Republicans voted on Tuesday, Romney raised more than $1.3 million at a luncheon in Chicago.

Illinois was the 28th state to hold a primary or caucus in the selection of delegates to the nominating convention, about halfway through the calendar of a Republican campaign that has remained competitive longer than most.

A change in party rules to reduce the number of winner-take-all primaries has accounted for the duration of the race. But so has Romney's difficulty in securing the support of the most conservative of the GOP political base. Santorum and Gingrich have struggled to emerge as the front-runner's sole challenger from the right.